Home
Class 12
MATHS
If the sum of the coefficient in the exp...

If the sum of the coefficient in the expansion of `(alpha^2x^2-2alphax+1)^(51)` vanishes, then find the value of `alpha`

Text Solution

Verified by Experts

We have `(alpha^(2)x^(2)-3alphax+2)^(51)`.
`:.` Sum of coefficients `= (alpha^(2)-3alpha+2)^(51)`
Since sum of coefficient is zero,
`alpha^(2) - 3alpha + 2 =0`
`rArr (alpha+2)(alpha-1)=0`
`rArr alpha = 1,2`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Example|10 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 8.1|17 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

Similar Questions

Explore conceptually related problems

The sum of the coefficient in the expansion of (1+ax-2x^(2))^(n) is

The sum of the coefficient in the expansion of (1 + x+x^2)^n is

The sum of the coefficients in the expansion of (1+x-3x^2)^(171) is

If the sum of the coefficients in the expansion of (2x+3cx+c^(2)x^(2))^(12) vanishes, then absolute value of sum of the values of c is

Find the sum of the coefficients in the expansion of (1+2x+3x^2+ n x^n)^2dot

If the sum of the coefficient in the expansion of (alpha x^(2) - 2x + 1)^(35) is equal to the sum of the coefficient of the expansion of (x - alpha y)^(35) , then alpha =

The sum of the coefficients in the expansion of (1 - x + x^(2) - x^(3))^(n) ,is

If ac lt b^2 then the sum of the coefficient in the expansion of (a alpha^2 x^2+ 2b alpha x+c)^n is (a, b,c, alpha in R and n in N)

Find the coefficient of x^(6) in the expansion of (1-2x)^(-5//2) .

If the sum of coefficients in the expansion of (x-2y+3z)^n is 128, then find the greatest coefficient in the expansion of (1+x)^ndot